A multi-generational family card game that has captivated players for decades - now with computational analysis to discover just how special that "once in a lifetime" moment truly is!

This repository contains the computational analysis of a beloved family solitaire game passed down through generations. What started as a friendly family debate about the difficulty of achieving victory led to one of the most extensive card game probability studies ever conducted - with over 700 million simulated games!

The catalyst? A confident family member claimed to have won "several times" and found it "boring." With 40+ years of gameplay experience and a background in quantitative analysis, the challenge was set: prove just how extraordinary a win truly is.

Once In A Lifetime is a solitaire card game where the ultimate goal is to consolidate all 52 cards into a single stack. The name perfectly captures the rarity of this achievement - as our extensive computational analysis reveals!

• Start with a standard 52-card deck, shuffled
• Your goal: Get all cards into one stack

1. Initial Play: Draw and place the first card face-up ♠️

2. Draw and Compare: Draw the next card from the deck

3. Matching Logic: The new card is compared to existing stack tops using these rules:

   • Cards match if they have the same rank OR same suit
   • New cards can match with stacks in two specific positions only:
     • Adjacent stack (immediately to the left)
     • Stack exactly 3 positions back (3 positions to the left)

   Position Rule Example (with stacks Z, C, Y, X from left to right):

   Z    C    Y    X
   ♠️K  ♦️5  ♣️7  [New Card: ♠️A]
   
   ♠️A can match with:
   ✅ Y (adjacent): ♠️A vs ♣️7 = No match
   ✅ Z (3 back): ♠️A vs ♠️K = Same suit! Match!
   ❌ C (2 back): Not allowed by rules
   

4. Player Choice: If both positions have matches, player chooses one (but not both)

5. Stack Consolidation: When cards match, place the new card on top:

   Before: ♠️K  ♦️5  ♣️7  
   After:  ♠️A  ♦️5  ♣️7
           ♠️K
   

6. Cascading Matches: After any match, check if stacks can now merge using the same position rules

7. No Match Rule: If no valid match exists (adjacent OR 3-back), create a new stack to the right

8. Scoring: Continue until all 52 cards are drawn. Count your final stacks - fewer is better!

# Run the latest, most complete version
python OiaLver0.0.5.py

# Try the clean, object-oriented version
python GoodOne2.py

# These will run 10,000 simulations by default

# For serious statistical analysis
julia OnceInALifetime.jl 1000000    # 1 million games
julia OnceInALifetime.jl 1000000000 # 1 billion games!

# Standard version with plotting
julia OiaLver0.0.5.jl

• Python: matplotlib for visualizations
• Julia: Random, Plots packages

Using high-performance Julia code, we conducted one of the largest solitaire simulations ever:

• 700+ million games simulated
• Multiple implementations to verify accuracy
• Statistical analysis of score distributions
• Performance optimization achieving 240,000+ games/second

After 700 million simulations:

• 🏆 Wins achieved: 0
• 📊 Upper bound probability: Less than 1 in 700 million
• 🎯 Conclusion: "Once In A Lifetime" is perfectly named!

🎯 2 stacks: ████ 0.18%  (1,830 games) - LEGENDARY!
📊 3 stacks: ████████████████ 13.28%  - Exceptional
📈 4 stacks: ████████████████████████████████████████ 46.50% - Great!
📈 5 stacks: ████████████████████████████ 31.73% - Good!
📉 6+ stacks: ██████ 8.31% - Keep playing!

• OiaLver0.0.5.py - 🌟 Most complete with matplotlib histograms
• GoodOne2.py - 🎯 Clean, object-oriented design
• OiaLver0.0.1.py to 0.0.4.py - 📚 Evolution of development
• Alternative versions - Various approaches and experiments

• OnceInALifetime.jl - 🚀 High-performance simulation engine
• OiaLver0.0.5.jl - 📊 Full-featured with plotting capabilities

• OnceInALifetime.qmd - 📝 Complete narrative and analysis
• CLAUDE.md - 🤖 AI development guidance

from OiaLver0_0_5 import main
main(iterations=1)  # Play one game and see your score!

main(iterations=100000)  # Analyze 100K games

main()  # Run until first win (could take a VERY long time!)

1. Restrictive Position Rules: Cards can ONLY match adjacent OR exactly 3 positions back - no other positions allowed
2. Limited Matching Options: Only rank OR suit matching
3. Sequential Dependencies: Card order matters tremendously
4. Cascade Complexity: Matches can trigger chain reactions, but still follow strict position rules
5. Choice Constraints: When both positions have matches, choosing one eliminates the other opportunity
6. Probabilistic Convergence: Getting close requires multiple rare events aligning perfectly

• 52! possible deck arrangements: 8.07 × 10⁶⁷ combinations
• Complex state space: Each card placement creates branching possibilities
• Convergence requirements: Multiple perfect matching sequences needed
• Statistical significance: 700M+ samples provide robust probability bounds

Our computational analysis definitively proves that achieving a "Once In A Lifetime" victory is:

✨ Extraordinarily rare - Less than 1 in 700 million chance
🎯 Perfectly named - The game title captures the true rarity
🧬 Statistically fascinating - A beautiful example of complex probability
👨‍👩‍👧‍👦 Family legend confirmed - 40+ years of gameplay experience validated!

While winning is incredibly rare, this makes the game:

• Endlessly replayable - Every game offers hope!
• Statistically fascinating - Each attempt contributes to understanding
• Family bonding material - Shared challenge across generations
• Computational showcase - Demonstrates the power of simulation
• Mathematical beauty - Probability theory in action

Feel free to:

• 🔧 Optimize the algorithms further
• 📊 Add new visualization features
• 🧪 Experiment with rule variations
• 📈 Extend the statistical analysis
• 🎮 Create interactive versions

This family card game simulation is shared freely - may it bring joy and statistical wonder to your household too!

"The best part about a 1-in-700-million chance? It's not zero!" 🎲✨